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Popular >

derivative of y= 1/(cos(x/2))

Solution

derivative of

y = \frac{1}{cos ( \frac{x}{2} )}

Solution

sec (\frac{x}{2}) tan (\frac{x}{2}) \frac{1}{2}

Solution steps

\frac{d}{d x} (\frac{1}{cos ( \frac{x}{2} )})

Simplify

\frac{1}{cos ( \frac{x}{2} )} : sec (\frac{x}{2})

= \frac{d}{d x} (sec (\frac{x}{2}))

Apply the chain rule:

sec (\frac{x}{2}) tan (\frac{x}{2}) \frac{d}{d x} (\frac{x}{2})

= sec (\frac{x}{2}) tan (\frac{x}{2}) \frac{d}{d x} (\frac{x}{2})

\frac{d}{d x} (\frac{x}{2}) = \frac{1}{2}

= sec (\frac{x}{2}) tan (\frac{x}{2}) \frac{1}{2}

Popular Examples

integral of 216x^2cos(6x)

\int 216 x^{2} cos (6 x) d x

(\partial)/(\partial y)(x^{2/3}y^{1/3})

\frac{\partial}{\partial y} (x^{\frac{2}{3}} y^{\frac{1}{3}})

limit as x approaches 3 of-3/7 x+4/11

x \to 3 lim (- \frac{3}{7} x + \frac{4}{11})

derivative of x^2e^x-2xe^x+2e^x derivative of

x^{2} e^{x} - 2 x e^{x} + 2 e^{x}

y^{''}-10y^'+26y=4

y^{^{''}} - 10 y^{^{'}} + 26 y = 4

Frequently Asked Questions (FAQ)

What is the derivative of y= 1/(cos(x/2)) ?
The derivative of y= 1/(cos(x/2)) is sec(x/2)tan(x/2) 1/2
What is the first derivative of y= 1/(cos(x/2)) ?
The first derivative of y= 1/(cos(x/2)) is sec(x/2)tan(x/2) 1/2